"The world may seem orderly, but randomness and chaos shape everything in the universe, from enormous galaxies all the way down to subatomic particles. Take a chilly window sheeting over with ice: even one oddly shaped snowflake can exert an influence on the final frosty pattern. Understanding how random fluctuations can ripple out to produce global effects is what French mathematician Vincent Vargas of the University of Geneva in Switzerland set out to do more than 10 years ago."
"Now mathematicians have proved the conjecture using an insightful technique that should open the door for understanding much more complex systems. The conjecture involves the behavior of a form of randomness found in a huge range of fields, from quantum chaos to Brownian motion to air turbulence. Mathematicians use a mathematical measuring tape called Gaussian multiplicative chaos, or GMC, to pick out subtle patterns hidden inside an otherwise impenetrable sea of randomness."
Randomness and chaos shape systems from galaxies to subatomic particles, and tiny local fluctuations can determine global patterns. Vincent Vargas developed ideas over a decade ago that, together with Christophe Garban, crystallized in the Garban-Vargas conjecture in 2023. Mathematicians have now proved the conjecture using an insightful technique that promises access to more complex systems. The conjecture concerns Gaussian multiplicative chaos (GMC), a tool for extracting subtle patterns from random fields across quantum chaos, Brownian motion, turbulence, and number theory. Jean-Pierre Kahane first developed GMC in 1985, and renewed interest has made the topic central in probability theory.
Read at www.scientificamerican.com
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